# Questions tagged [fourier-transform]

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### Fourier pseudo-spectral method and numerical dissipation

Performing a direct numerical simulation of isotropic turbulence with Fourier pseudo-spectral method (Orzag & Patterson, PRL, 1972) using FFT. For a background of the method, which is widely used ...
8k views

### Least Squares and Fourier Series

I have a little bit of problem figuring out the relation between Fourier series and Least Squares. As far as I understand, LS is a way of minimizing the quadratic error between a measured value $y_i$ ...
14k views

### C++ libraries for Fast Fourier Transform in high precision

I am looking for a C++ library for Fast Fourier Transform (FFT) in high precision (e.g., using high precision real data types similar to mpfr_t in MPFR or ...
2k views

### Fourier Transform of function in Spherical Harmonics

I have a function $f(r,\theta,\phi)$ which I am expressing in terms of spherical harmonics $$f(r,\theta,\phi) = \sum_{l=0}^{\infty} \sum_{m=-l}^{l} g_{l,m}(r) d_{l,m}(\theta,\phi)$$ where $d_{l,m}$...
97 views

### Discrete sine and cosine transform for mixed derivatives

Using sine and cosine transforms to solve Poisson's equation with Dirichlet boundary conditions seem quite standard nowadays (see, e.g., here or Table 2 in this paper). In the case of Poisson's ...
558 views

### How to use matlab command 'fft' to solve Ax=b arising from Poisson equation?

I want to ask a question about fast solver to the Poisson equation with Homogenous boundary conditions as follows: $$-\Delta u = f.$$ After centered difference using $n+2$ equidistance points in all ...
148 views

### How to define a dimensionless Objective function for determining how peaked a curve is?

I have attached 2 plots for FFT spectra. One is considered good and one is bad. The good one is classified on the basis of how closely spaced the frequencies and the bad is based on how multiple ...
153 views

302 views

### MPI support for discrete Fourier transform (DFT) in Python

I am looking for a discrete Fourier transform (DFT) library that can be run with MPI on Python. Usually, in other languages (C, Fortran) FFTW is used. There's a Python wrapper for FFTW called pyFFTW, ...
184 views

### How to get Fourier transform of Fisher-Kolmogorov?

How can I use Fourier Transform to solve Fisher-Kolmogorov Equation in 1D? \begin{equation} u_t(x,t) = u_{xx}(t) + u(1-u) \end{equation} \begin{equation} u(0,x) = \phi(x) \end{equation} with ...
330 views

### How to obtain values in physical space for a given spectrum?

My question falls under purview of turbulent flows. I want to add an initial perturbation, for which I have a given energy spectrum (say$E(k)=ak^4e^{-bk^2}$). The steps involved in getting these ...
861 views

### Numerically computing the advection equation

I am trying to write a program to compute the advection equation. $$u_t +u_x = 0$$ I use the spectral method for the spatial derivative $u_x$ and the leapfrog method for the time derivative $u_t$. ...
419 views

### How do I avoid divide-by-zero when solving the Poisson equation with Fourier transforms?

I wanted to try to implement part of the method in the following article using Fourier transforms. http://www.shodor.org/media/content/jocse/student_submissions/nocito2010/nocito2010_pdf Right now I ...
643 views

### FFT on non-orthogonal lattice ( for computing convolutions and solving PDEs )

I saw many examples of application of FFT for computation of convolutions and solving PDEs ( like Poisson equation ). It is very strightforward and efficient if I work with rectangular (orthogonal) ...
681 views

### Calculating high-order derivatives using FFT in Matlab

I'm trying to calculate the derivative of a function using FFT in Matlab. I've coded the following function to calculate it: ...
110 views

### Fourier spectral method for coordinate transformed heat equation

As the title said, I want to solve a coordinate transformed heat equation using fourier spectral method. In particular, I am interested in transforming an uniform grid into an adaptive non-uniform ...
60 views

### FFT of “implicitly” uniform data

I am trying to take a Fourier transform of a density field estimated from mock galaxy survey catalogs. Basically, you start with a list of galaxy positions, then you bin these positions over some ...
426 views

### Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
156 views

### Approximating improper integral with FFT

In d'Halluin et al. (2005) (http://imajna.oxfordjournals.org/content/25/1/87.short) the authors claim that the correlation integral $$I(x) = \int_{-\infty}^{\infty} V(x+y) f(y) dy$$ can be ...
18 views

### Normalising DFTs Correctly

I have been playing around with convolutions in scipy's signal package: ...
29 views

### Palmprint Identification - Why do we align the images before we use the Fourier Transform?

I am currently reading the paper PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM by WENXIN LI, DAVID ZHANG and ZHUOQUN XU about identifying persons based on an image of their palm, one version of the ...
214 views

### Solving a 3D (almost radial) convolution with FFT

I have a 3D integral that is almost a radial convolution of the form $$\int d^{3}k'h(\mathbf{k'})g(|\mathbf{k-k'}|)$$ and I am looking for a fast and efficient algorithm (e.g. FFT) to solve it ...
216 views

### Amplitude at a given frequency in a wide band signal

Could anyone suggest the most computationally efficient method for finding amplitude at a given frequency having a noisy wide band signal. To be more specific about a task. I have some physical ...
44 views

### Constructing 2 fold oversampled cosine basis in MATLAB

So I'm trying to construct a 2 fold oversampled cosine basis in MATLAB. I know how to construct the basis as a square matrix using the following command: ...
658 views

### Fast Forward Laplace transform

There are examples for fast numerical inversion of the Laplace transforms. For example here: http://www.mathworks.com/matlabcentral/fileexchange/32824-numerical-inversion-of-laplace-transforms-in-...
208 views

### Fast way to compute integral of type $\int dx f(x) \cos(n \pi x)$ in SciPy

I have an integral of the form $$I(n) = \int_0^1 dx f(x) \cos(n \pi x) ,$$ where $n$ is an integer. In other words, I calculate the cosine Fourier coefficients of function $f$, which is real and ...
428 views

### Numpy FFT gives me a pulse shorter than it should be. Not sure what I am doing wrong

I've created a code (Python, numpy) that defines an ultrashort laser pulse in the frequency domain (pulse duration should be 4 fs), but when I perform the Fourier Transform using DFT, my pulse in the ...
64 views

### Obtain velocity from imposed energy spectrum using the inverse FFT

I am trying to obtain the spatial representation of $u(x)$ (e.g. velocity) from its energy spectrum $E(k)=k^4\exp(-(k/k_0)^2)$, which is given in the frequency domain, provided $|u(k)|=\sqrt{2E(k)}$. ...